In R package jointseg ([1]}), they provide two real datasets GSE11976 and GSE29172 to resample from, where the truth of changepoints is already known. However, since we do not have the information about the true value of \({\gamma }^{\star }\)  on each segment, it is impossible to compute the pseudo Hellinger distance between each estimator and the truth. Note that for both GSE11976 and GSE29172 datasets, we need to choose the tumour fraction when resampling from them. We consider the tumour fraction levels 0.79 and 1 for the dataset GSE11976 and the levels 0.7 and 1 for GSE29172 which turns out to be the situations where the size of each jump at the changepoint is relatively large as indicated in Figure 9 of [2]}. Therefore, we can roughly evaluate the performance of each estimator by its frequency of correctly estimating the number of changepoints. Although our selection procedure can be applied in the scenario where small amount of outliers present in the observations, as we have seen in Section  some candidates in \(\widehat{\Gamma }\)  are sensitive to the outliers. To avoid the phenomenon that an estimator systematically underestimates the number of changepoints but due to the sensitivity to outliers it accidentally gives a correct number of segments, we run a smooth procedure on the data before applying all the estimation procedures by implementing the function smooth.CNA from the famous R package DNAcopy. Moreover, since we have seen in the simulation study that the performance of CBS and cumSeg is quite poor, we remove these two estimators from our candidates set \(\widehat{\Gamma }\)  for simplicity. For each dataset and each level of tumour fraction, we simulate 1000 profiles of length \(n=1000\)  with 5 changepoints where the length of each segment is at least 20. The results are shown in Table REF . As one can observe, among the state-of-art ones, robseg (biweight) is the best for correctly estimating the number of changepoints on this dataset. By running a data-driven procedure to select among the candidates set \(\widehat{\Gamma }\) , our selected estimator ES shows a competitive performance in this situation as compared to the best one robseg (biweight).
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